

A088431


Half of the (n+1)st component of the continued fraction expansion of sum(k>=1,1/2^(2^k)).


5



2, 1, 2, 2, 3, 2, 1, 2, 3, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 2, 3, 1, 2, 3, 2, 2, 1, 3, 2, 1, 2, 2, 3, 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 2, 3, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 3, 2, 1, 2, 2, 3, 2, 1, 2, 3
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OFFSET

1,1


COMMENTS

To construct the sequence use the rule : a(1)=2 then a(a(1)+a(2)+...+a(n)+1)=2 and fill in any undefined places with the sequence 1,3,1,3,1,3,1,3,1,3,1,3,.....
Contribution from Dimitri Hendriks, May 06 2010: (Start)
This sequence appears to be the sequence of run lengths of the regular paperfolding sequence A014577, i.e. the latter starts as follows: 2 zeros, 1 one, 2 zeros, 2 ones, etc. (End)


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192


FORMULA

a(n)= (1/2)*A007400(n+1); a(a(1)+a(2)+...+a(n)+1) = 2.


EXAMPLE

Example to illustrate the comment : a(a(1)+1)=a(3)=2 and a(2) is undefined. The rule forces a(2)=1. Next, a(a(1)+a(2)+1)=a(4)=2, a(a(1)+a(2)+a(3)+1)=a(6)=2 and a(5) is undefined. The rule forces now a(5)=3.


PROG

(Scheme) (define (A088431 n) (* 1/2 (A007400 (+ 1 n)))) ;; Code for A007400 given under that entry.  Antti Karttunen, Aug 12 2017


CROSSREFS

Cf. A007400, A014577, A088435, A092910.
Sequence in context: A134192 A284044 A126305 * A254661 A052304 A049874
Adjacent sequences: A088428 A088429 A088430 * A088432 A088433 A088434


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Nov 08 2003


STATUS

approved



